ISIS fighters seen in a video posted by the group's al-Furqan media unit

Screengrab via AFP

Iraq's prime minister has warned residents of the embattled city of Fallujah to drive out insurgents or face a military assault, suggesting a serious military attack on Fallujah could be imminent.

Nouri al-Maliki, a Shiite Muslim whose government has little support in Sunni-dominated Fallujah, called on tribal leaders to drive out militants who last week seized key towns in the desert leading to the Syrian border.

The terrorist group, known as the Islamic State of Iraq and the Levant (ISIS), seized control of Fallujah last week in a direct challenge to the authority of the Shia-led Iraqi government.

Iraqi forces have now reportedly surrounded the city and reinforcements are arriving from nearby Baghdad.

The US says it is speeding up the delivery of Hellfire missiles and surveillance drones to help the Iraqi government fight the militants.

In a televised statement, Mr Maliki said Fallujah would be spared an attack if the terrorists were expelled.

"The prime minister appeals to the tribes and people of Fallujah to expel the terrorists from the city in order to spare themselves the risk of armed clashes," the statement said.

Two local tribal leaders said meetings were being held with clerics and community leaders to find a way to persuade the ISIS fighters to leave.

But defiant militants issued a video declaring that: "The revolutionaries of Fallujah tribes are resolved to punish those who are linked to the sectarian government."

Mr Maliki promised the army would not attack residential areas in Fallujah, which is some 40 kilometres west of Baghdad's main airport.

But any assault would have echoes of US assaults on the city in 2004.

Security officials said Mr Maliki, who is also commander-in-chief of the armed forces, had agreed to hold off an offensive for now at least to give tribal leaders in Fallujah more time to drive out the Sunni Islamist militants on their own.

"No specific deadline was determined, but it will not be open-ended," a special forces officer said of plans to attack.

"We are not prepared to wait too long. We're talking about a matter of days only.

Professor Amin Saikal, the director of Australian National University's Centre for Arab and Islamic Studies, says Mr Maliki's government is in weak position.

"It seems that he does not have full control over some outlying areas and country," he said.

"In some ways Iraq has already become Balkanised in a sense, the Kurdish - who make up 20 per cent of the country - has established an extensive autonomous state in the north of Iraq which often operates independent of the centre.

"Al-Maliki has the backing of the Shiites and particularly some important elements of the Shiites and, of course, he also has got very close relationship with Iran.

"But whether you will be able to overcome this challenge from the Al Qaeda-linked groups and their Sunni supporters that remains to be seen."

In Ramadi, tribal groups join offensive against ISIS

ISIS has emerged in Syria's civil war as an affiliate of the international Al Qaeda network and a powerful force among Sunni Muslim rebels seeking to oust president Bashar al-Assad.

In Iraq, it has been tightening its grip on Anbar province, a thinly populated, mainly Sunni region the size of Greece, and on the area's main towns, strung along the Euphrates river.

Its fighters in Fallujah have been flying black flags associated with Al Qaeda.

The group's resurgence has divided people in Anbar, where many accuse Mr Maliki of shutting Sunnis out of power and being a pawn of Shiite Iran. Some sympathise with and support the Islamist militants, or are too fearful to move against them.

"We are going to have an important meeting this evening and that will include some Al Qaeda fighters in Fallujah to convince them to leave the city and deprive Mr Maliki of a pretext to push his army inside the city," one tribal leader said.

"We should make Al Qaeda fighters understand that their staying in Fallujah will create rivers of blood."

ISIS fighters have also moved in to Ramadi, west of Fallujah, but there they are opposed by tribesmen allied to the government.

On Monday clashes broke out west of Ramadi at dawn as militants battled special forces who were backed by tribesmen.

"This combat has been going on with a well-trained and a highly organised Al Qaeda group," an Iraqi special forces officer said, adding there were foreign fighters among the militants.

"When we defeat it, the balance of power in the whole of Anbar province will change".

ISIS's stated aim has been to create a Sunni state straddling the border into Syria's rebel-held desert provinces.